Pullback of the Normal Module of Ideals with Low Codimension

Author:

Miranda-Neto Cleto B1

Affiliation:

1. Universidade Federal da Paraíba, João Pessoa, 58 051-900 PB, Brazil

Abstract

Abstract The normal module (or sheaf) of an ideal is a celebrated object in commutative algebra and algebraic geometry. In this paper, we prove results about its pullback under the natural projection, focusing on subtle numerical invariants such as, for instance, the reduction number. For certain codimension 2 perfect ideals, we show that the pullback has reduction number two. This is of interest since the determination of this invariant in the context of modules (even for special classes) is a mostly open, difficult problem. The analytic spread is also computed. Finally, for codimension 3 Gorenstein ideals, we determine the depth of the pullback, and we also consider a broader class of ideals provided that the Auslander transpose of the conormal module is almost Cohen–Macaulay.

Funder

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Fundação de Amparo à Pesquisa do Estado de São Paulo

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

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